308 



The Astronomer Royal on a supposed [April 25, 



Combination, arising from the coexistence of different things, objectively 

 or subjectively, in the same aggregate ; 



Consistency, arising from the coexistence of different events affirmed by 

 different assertions. 



Succession generates : Logical inference, Sequence in Space, in Time, 

 and in Action. 



Mixed cases arise from combining assertions of different kinds. 



Composition, combination, and consistency only are considered in the 

 present paper. Composition constitutes the primary, and consistency the 

 secondary propositions of Boole. Combination has not been distinctly re- 

 cognized in logical works, but is constantly implied in Boole's and De 

 Morgan's treatments of Composition, whereby its real character has been 

 overlooked. Logical Inference is partially considered in the treatment of 

 Composition, Combination, and Consistency. Sequence in Space, Time, 

 and Action is not treated at all. 



Thomson's, De Morgan's, and Boole's notations are carefully interpreted. 

 Particular attention is paid to Boole's results for Consistency, and the 

 nature of the error which he committed in accommodating those results to 

 Composition, together with the value of his accommodated results, is 

 exactly determined. The ascertainment of these errors by a fundamental 

 reconsideration of the bases of the relations of Composition and Con- 

 sistency, and a purely logical method of obtaining precise results, forms 

 the distinctive character, as it was the special object, of the present in- 

 vestigation. 



II. u On a supposed Periodicity in the elements of Terrestrial Mag- 

 netism, with a period of 26-J- days." By George Biddell Airy, 

 Astronomer Royal. Received March 26, 1872. 



In a paper published in the ' Proceedings of the Imperial Academy of 

 Sciences of Vienna,' vol. lxiv., Dr. Karl Hornstein has exhibited the results 

 of a series of observations which appeared to show that the earth's 

 magnetism undergoes a periodical change in successive periods of 26-J- 

 days, which might with great plausibility be referred to the rotation of 

 the sun. 



It appeared to me that the deductions from the magnetic observations 

 made at the Royal Observatory of Greenwich, and which are printed 

 annually in the ' Greenwich Observations/ or in the detached copies of 

 ■ Results of Magnetical and Meteorological Observations made at the 

 Royal Observatory of Greenwich/ would afford good materials for testing 

 the accuracy of this law, as applicable to a series of years. The mean 

 results of the measured hourly ordinates of the terrestrial magnetic ele- 

 ments are given for every day, and it is certain that there has been no 

 change of adjustments of the declination and horizontal-force instruments 

 in the course of each year. For the horizontal-force instrument the tern- 



